Appendix C. Details of methods for estimating meadow selection and home range size.

C.1 Meadow selection

We performed a seasonal patch selection analysis (sensu a Step Selection Function; Fortin et al. 2005, Dancose et al. 2011) to test how individual bison choose between profitable meadows and previously visited meadows over time. We used three hour location data for the 33 female bison collared between 2005 and 2013. Using these data, we focused on two seasons: summer (May through the second week in August) and winter (second week in November through April). We removed the autumn season because bison spend between 6 and 37% of their time outside of the park during this time of the year.

To render GPS location data to such a patch selection framework, we followed the methods of Merkle et al. (2014), and identified every incidence when an individual departed a meadow (i.e., the source meadow) and then entered a different meadow (i.e., target meadow), hereafter referred to as patch-to-patch movement. For each patch-to-patch movement (n = 11,011 in summer; n = 14,466 in winter), we generated a sample of 20 possible meadows that the animal could have chosen from the source meadow, which were then compared to the observed target meadow. The 20 possible target meadows were generated based on distance weighted by the resource-independent movement kernel (Forester et al. 2009) among patch-to-patch movements for bison.

C.2 Home range size

For meadow choice strategies that varied with density, we assessed how they affected individual spatial distribution by testing whether individual variation in random coefficients influenced seasonal home range size. Since the patch selection analysis excluded the relatively poor quality GPS collar data from the 1990s, we recalculated home range sizes using all three hour data collected for each individual. Again using the reference technique (Worton 1989), we used fixed smoothing factors of 1068 and 1653 m for summer and winter respectively, and calculated home range size as the 95% contour of each individual’s kernel. We excluded individual animals within a season if they were missing >1 month of GPS data.